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Deriv Compl Full Rewri 33144 pair #381921957
details
property
value
status
complete
benchmark
t008.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.1210021973 seconds
cpu usage
83.186477211
max memory
8.5839872E7
stage attributes
key
value
output-size
9312
starexec-result
WORST_CASE(?,O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_tct_dc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^2)) * Step 1: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) log(s(x)) -> s(log(half(s(x)))) s(log(0())) -> s(0()) - Signature: {half/1,log/1,s/1} / {0/0} - Obligation: derivational complexity wrt. signature {0,half,log,s} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind triangular matrix interpretation: Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [0] p(half) = [1] x1 + [0] p(log) = [1] x1 + [1] p(s) = [1] x1 + [0] Following rules are strictly oriented: s(log(0())) = [1] > [0] = s(0()) Following rules are (at-least) weakly oriented: half(0()) = [0] >= [0] = 0() half(s(0())) = [0] >= [0] = 0() half(s(s(x))) = [1] x + [0] >= [1] x + [0] = s(half(x)) log(s(x)) = [1] x + [1] >= [1] x + [1] = s(log(half(s(x)))) * Step 2: WeightGap WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) log(s(x)) -> s(log(half(s(x)))) - Weak TRS: s(log(0())) -> s(0()) - Signature: {half/1,log/1,s/1} / {0/0} - Obligation: derivational complexity wrt. signature {0,half,log,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = NoUArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind triangular matrix interpretation: Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [0] p(half) = [1] x1 + [5] p(log) = [1] x1 + [2] p(s) = [1] x1 + [0] Following rules are strictly oriented: half(0()) = [5] > [0] = 0() half(s(0())) = [5] > [0] = 0() Following rules are (at-least) weakly oriented: half(s(s(x))) = [1] x + [5] >= [1] x + [5] = s(half(x)) log(s(x)) = [1] x + [2] >= [1] x + [7] = s(log(half(s(x))))
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